Published in the Proc. of the Nat. Conf. on Industrial Problems on Machines and Mechanisms,
IIT Kharagpur, Feb.24-25, 2005, pp. 197-203.
Finite Element Modeling of Carpet Weaving Loom Structure
Himanshu Chaudhary and S.K. Saha
Department of Mechanical Engineering
Indian Institute of Technology Delhi
Haus Khas, New Delhi-110016, India
[email protected]; [email protected]
Tel: (011) 2659 1135/6320; Fax: 2658 2053
Abstract
Handmade carpet industry needs upgradation in weaving technology to meet the demand of quality carpets and
the rate of production. Present looms to weave the carpets are made of wood, which are susceptible to termite
attacks. The use of wood also causes deforestation. Moreover, the high tension required in the warps is
generated by pulling a rope. This requires about 40-45 minutes by 2 -3 persons. The traditional practice of
generating high tension is laborious and demands a change. In order to avoid the above difficulties, an improved
metallic loom has been proposed elsewhere which made weaving easy but the cost of loom is high. In the
improved loom, worm and worm-wheel, and ratchet-pawl are used to develop tension in the lower beam and to
lock the upper beam, respectively. In this paper, finite element analysis of the metallic loom is carried out to
determine the critical stresses and deflection in its components so that optimum sizes and shapes of the
s tructural members can be selected.
Keywords: Carpet loom, Finite element method, and Structure.
1. Introduction
Handloom weaving of carpets is different in many aspects from the handloom weaving of the fabric [1].
Handloom weaving of fabric almost replac ed by sophisticated power looms but not the same has happened to
the carpet weaving because of its inherent knotting system and aesthetic values associated with it. The oriental
carpet, as shown in Fig. 1, is generally woven on a warp fixed almost vertically in front of the weaver. Required
length of warp threads wrapped over upper beam called warp beam that supported by a pair of columns, about
1.8 m high. Tuft of wool or silk inserted between the warp threads, knotted it in with weft and warp, as
illustrated in Fig. 2. The process continues along the whole row. Then, the row is pressed using a tool called
beater [1]. Carpet knotting continues according to the carpet design. Traditionally, oriental carpets are woven on
wooden looms ( Fig. 1), which are becoming economically, environmentally and functionally non-viable due to
the following reasons [2-3]:
• Life is limited (5-8 years) due to susceptibility to termites and frequent investments are required;
• Deforestation;
• Need rope arrangement to generate high t ension in the warps, which is laborious; and
• Over the time the wooden beams bend causing non-uniform tension in the warps. Hence, the carpet
quality is affected.
With wooden looms, carpet weaving for large width becomes difficult because greater effort is required to put
the warp threads in high tension. Tensioning requires 2 -3 persons who pull a rope to rotate the beams, as shown
in Fig. 2. Since there is no mechanical advantage in pulling the rope, the tensioning job is very tedious, and
requires about 30- 40 minutes. Moreover, in addition to the low life and deforestation, they are prone to
accidents due to the damages done by the termites. Existing wooden components have evolved over the years
based on the weavers’ experiences. There is no literature reporting any systematic design of such components
except in by one of the authors of this paper [3]. In order to overcome the problems of existing wooden looms,
Saha et al. [3] designed and developed a metallic loom, as shown in Fig. 3, considering all aspects of carpet
weaving. The lower beam fitted with a worm and worm-wheel for developing tension in the warp threads. A
ratchet -pawl mechanism is used to lock the top (warp) beam. Main components of the metallic loom [3] are
shown in Fig. 3, where the upper and lower beams, and two side supports contribute to the 90% of the loom
weight and cost. In order to reduce the weight and cost, it is important to know the critical zones of the beams
and columns so that their sizes and shapes can be modified. In this pape r finite element analysis of this structure
Published in the Proc. of the Nat. Conf. on Industrial Problems on Machines and Mechanisms,
IIT Kharagpur, Feb.24-25, 2005, pp. 197-203.
is performed to locate the critical zones, whereas a modified design is proposed in a separate communications
[4].
The paper is organized as follows: Section 2 explains the function of the loom and the load modeling. In
section 3, finite element model and solution using standard FE tool are presented. Results for a typical metallic
carpet loom [3] are reported in Section 4, where they are compared with those of an optimized loom [4].
Fig. 1 Traditional oriental wooden handloom
2
5
1
8
4
6
3
7
1. Side Support; 2. Upper (Warp) Beam; 3. Lower (Cloth) Beam; 4. Weft Thread; 5.Warp Threads (Open Shed
Position); 6. Knotted Turf; 7. Rope for Tensioning; 8. Beating Direction.
Published in the Proc. of the Nat. Conf. on Industrial Problems on Machines and Mechanisms,
IIT Kharagpur, Feb.24-25, 2005, pp. 197-203.
Fig. 2 Schematic diagram of o riental loom with rope tensioning
1. Support Channel; 2. Base Channel; 3. Ratchet and pawl; 4. Upper (Warp) Beam; 5. Shedding Pipe; 6.
Tensioning Device; 7. Lower (Cloth) Beam; 8. Handle; 9. Shedding Roller; 10. Bush Bearing.
Fig. 3 Improved carpet loom [3]
2. Loom Components and Their Function
In textile terminology, the part that is used to wind the warp threads and carpet are called beams, namely, the
upper (warp) and lower (cloth) beams, 4 and 7 of Fig. 3, respectively. Their function is, however, very complex
[5]. Functionally, the warp- beam gradually delivers equal amount of length to all warp threads as the carpet
weaving progresses, and maintain proper tension in all the wrap threads. The beam is locked between two let off
action to provide proper tension. Still there is a variation in tension of the warp threads during shedding motion,
which affects the quality of the carpet. In the improved metallic loom [3], a worm and worm-gear mechanism is
used on the right side of the lower beam, 6 of Fig. 3, to provide tension to the warp threads, while a pair of
ratchet -pawl, as the left set is indicated with 3 in Fig. 3, is used to lock the upper beam. Among others, two main
components of the loom are beams and side columns. The function and constraints of the beams are given in
Table 1, which will allow us to model the loom appropriately.
Table 1 Warp and cloth beams’ functions and constraints
Function
Resist bending and
torque
Constraints
Kinematic: Let off equal length to all warp threads and lock for forward motion
during weaving
Geometric: Length of the beam is greater than the width of carpet
Strength: Support warp threads tension, and lock torsion without failing
Stiffness : Less deflection to maintain uniform tension in all the threads
Columns that support both the upper (warp) and lower (cloth) beams are under complex 3-dimensional
loading. The left column is indicated by 1 in Fig. 3. The tension in the warp threads is provided by worm and
worm- wheel, 6 of Fig. 3, that is attached to the bottom beam. As illustrated in Fig. 4, l ocking moment, M L, and
axial compressive load, P, act on the column. Additionally, friction force, F f, act on the column due to gradual
increase in tension of the wrap threads . Locking moment, M L, causes beam torsion, which depends on the
diameters of the beam and the locking devices, namely, ratchet at the upper beam and the worm-gear at the
Published in the Proc. of the Nat. Conf. on Industrial Problems on Machines and Mechanisms,
IIT Kharagpur, Feb.24-25, 2005, pp. 197-203.
lower beam. These loads increase simultaneously during tensioning and kinetic friction becomes zero after
completing the tensioning.
P
ML
1500 mm
Ff
P
300 mm
Fig. 4 Schematic diagram of a side support with worm and worm-wheel
2.1 Load Modeling
Warp threads made of cotton yarn were tested for breaking load on Textechono Statimat Me (a textile tester)
under standard textile testing conditions [6]. Average force/elongation curves for the warp threads are shown in
Fig. 5. Note that unlike conventional ductile metals like steel or aluminum, the cotton yarn does not have any
clear yield point. Like a brittle metal, e.g., cast iron, the yield point for cotton is obtained by drawing a tangent
line parallel to the line joining the origin to the breaking point [6]. The yield point of the thread occurred slightly
below the force, 9.81N (~1000g) at 5 percent elongation. Considering different yarn quality to be used in the
loom for which the yield force may lie within the range of 10N to 20N, the design load of 20N for each warp
thread is safe. Hence, the safety factor about two is assumed. Since all warp threads are wound uniformly over
the upper beam, as shown in Fig. 3, they are modeled as uniformly distributed load.
Published in the Proc. of the Nat. Conf. on Industrial Problems on Machines and Mechanisms,
IIT Kharagpur, Feb.24-25, 2005, pp. 197-203.
Fig. 5 Tens ile test results of warp threads
The load diagram of the upper beam, numbered as 4 in Fig. 3, during weaving is shown in Fig. 6. Since carpet
knotting to weave about six-inch carpet takes several days, the structure is subjected to steady loading. The
beam is supported on side columns and locked in the plane normal to the plane of the warp threads at A due to
the presence of ratchet and pawl, as seen in Fig. 3 from the front.
y
20 N/mm
A
x
B
x
1500 mm
50
Warp thread
direction
Fig. 6 Load diagram of the Upper (Warp) Beam
3. Finite Element Modeling
The upper and lower beams resist the thread load of 20 N/mm at 5 degree from the vertical plane, Fig. 6. This is
equivalent to the loads at the beam axis shown in Table2, whereas the beam and column sizes are shown in
Table 3. Uniaxial finite elements are appropriate for such components. Distance between the nodes, i.e., the
length of uniaxial elements, is chosen as 100mm which is about 6 percent of the length/height of beam/column.
The distance between the nodes is decided by the accuracy needed. Elements of the beam whose the crosssection is hollow circular are chosen as Pipe16 of ANSYS 7 and those for the columns whose the cross-section
is hollow square Beam4 is selected. Both the elements, Pipe16 and Beam4, have the capability to provide
tension, compression, torsion and bending. They allow six degree -of - freedom at each node, i.e, three
transnational and three rotational, as explained in Table 4 [7]. The load is applied at each node of the beam.
Note that the load carried by the corner nodes of the beam is half of that of the middle ones [8].
Published in the Proc. of the Nat. Conf. on Industrial Problems on Machines and Mechanisms,
IIT Kharagpur, Feb.24-25, 2005, pp. 197-203.
Table 2 Load per 100 mm length on beams
Components F y (N)
Fz (N)
M x (N- mm)
Upper Beam - 1992.4
174.3
117800
Lower Beam 1992.4
174.3
117800
F y: Force along Y; F z : Force along Z; M x : Moment about X.
Table 3 Sizes of the beams and columns [4]
Components
Beam
Cross- section
Hollow circular
Column
Hollow square
Size (mm)
OD=117.8
Wall thickness=3.8
Out side width=78.31
Wall thickness=1.41
Length/height (mm)
1500
1800
Table 4 Nodal DOF and load
Components
Beam
Type of
element
Pipe16
Column
Beam4
Node DOF
6- DOF: UX, UY, UZ, ROTX,
ROTY, ROTZ
6- DOF: UX, UY, UZ, ROTX,
ROTY, ROTZ
No. of
nodes
16
Middle nodal
loads
F x = -1992.4 N
F z= 174.3 N
M x= - 117800
N- mm
Corner nodal
load
F x= -1992.4/2 N
F z= 174.3/2 N
M x = 117800/2
N-mm
18
Now, the joint constraints are looked into. Joints at 3 and 6, Fig. 3, respectively, connect the beam to the
column using bush bearings. However, the ratchet -pawl and the worm and worm-gear are used to lock the
beams while tensioning needs to be developed. Thus, these joints are assumed to be fixed to the columns. The
joints, 8 and 10 of Fig. 3, are simply bush bearings whose width is less in comparison to the length of the beam.
Hence, they are modeled as cylindrical j oints of 2-DOF, i.e., the beam end is free to translate along and rotate
about the beam axis. Due to less width of the bearing, the stiffness of the two rotational constraints is very low.
Alternatively, these joints impose constraints on the translation normal to the warp thread plane. Hence, the
transnational stiffness perpendicular to the beam axis is assumed to be very high. An element Combin7 [7] is
chosen for this application. The Combin7 is the three -dimensional joint having joint flexibility (stiffness),
friction, damping, and certain control features. In order to use this element as the bush bearing connection
between the beam and column the following stiffness values used:
x- y translational stiffness (k1)= 10 9 N/m
z-direction stiffness(k 2)
= 0 N/ m
Rot- x and Rot -y stiffness (k3)= 0 N/m
where x, y, z are the local axes of the Combin7. Note that the z -axis of the Combin7 coincide with the axis of
rotation of the beam, i.e., global x axis. The lower ends of both the columns are grounded. So, these joints are
assumed to be rigid.
4. Results
The finite element model is developed and solved in Ansys7 [7]. The vector diagram of the deflection of the
loom is shown in Fig. 6, in which the maximum deflection, 18.97mm, occurs at the joint number 8 of Fig. 3.
The corresponding, von- Mises effective stress contour diagram is shown in Fig. 7. The maximum stress of
146.48 MPa is induced at the middle nodes of the beam. Moreover, the stress of 235.91 MPa is induced at the
joint 6 of the column, i.e., at the gear end of Fig. 3. In [4], the maximum stresses were computed analytically by
assuming the beams as simply supported, and columns as fixed-free end. Thus, the values were higher compared
to those obtained using the FE tool, i.e., ANSYS 7 as indicated in Table 5 .
Table 5 Comparision of FE solutions
Componets
Max. deflection Max. von- Mises effective Max. analytical
Published in the Proc. of the Nat. Conf. on Industrial Problems on Machines and Mechanisms,
IIT Kharagpur, Feb.24-25, 2005, pp. 197-203.
Beam
Column
18.97 mm
18.97 mm
stresses (ANSYS 7)
146.48 MPa
235.91 MPa
stresses [4]
150 MPa
240 MPa
Fig. 6 Vector deflection in the loom
Fig. 7 The von- Mises effective stress contours in the beams and columns
5
Conclusions
Published in the Proc. of the Nat. Conf. on Industrial Problems on Machines and Mechanisms,
IIT Kharagpur, Feb.24-25, 2005, pp. 197-203.
A metallic carpet loom developed to overcome the difficulties of the existing wooden looms is reported in Saha
et al. [3]. In order to reduce its weight and cost, optimization of its critical components, namely, the beams and
columns are carried out in [4]. For realistic estimation of the loads, tensile test of the warp thread was conducted
to obtain the load- deformation curve. Finite element analysis (FEA) of the components is carried out in this
paper to verify the stress and deflection results used for the optimized [4]. FEA is critical when the realistic
conditions are difficult to implement in analytical form [4], as was for the connection between beam and
columns. The FE model results are comparable with those from the analytical equations [4].
Acknowledgements
The research work reported here was possible due to the scholarship provided by the Government of India under
Quality Improvement Program, and the leave grant ed by M.L.V. Textile Institute, Bhilwara (Raj.) to the first
author. The help of those people from the Micromodel Lab., IIT Delhi, who provided information on the carpet
weaving and the metallic looms, is also acknowledged.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
S. M. William, Textile Industries, VI, The Gresham Publishing Company, London, (1935).
M. R. Saraf, Innovation in Design, Color and Texture Weaving Traditions and Modernity through
Technique, Report on First World Conference on Handmade Carpets, Nov. 4 -5, New Delhi, (2003), pp.
46 -5 0 .
S. K. Saha, R. Prasad, S. Sarange, and N. Shukla, Design and Development of Carpet Looms, Proc. of
11 t h Nat. Conf. on Machines and Mechanisms, Dec. 18- 19, IIT Delhi, (2003), pp. 739 -744.
H. Chaudhary, and S. K. Saha, Optimal design of an oriental carpet weaving loom structure, Trans. of
ASME, Journal of Mechanical Design, communicated, (2004).
A. Fannian, Handloom Weaving Technology, Van Nostand Reinhold Company, New York, (1979).
J. E. Booth, Principles of Textile Testing: An Introduction to Physical Methods of Testing Textile Fibers,
Yarns, and Fabrics, Temple Press, London, (1964).
ANSYS, Release 7.0, ANSYS Inc. (2003)
T. R. Chadrupatila, A. D. Belegundu, Introduction to Finite Elements in Engineering, Prentice Hall of
India Pvt. Ltd., New Delhi, (1996).